Arrange in descending order -
`2^(350), 5^(200), 3^(300), 4^(250)`

Options

A. `4^(250)gt 3^(300)gt 5^(200)gt 2^(350)`
B. `2^(350)gt 5^(200)gt 3^(300)gt 4^(250)`
C. `3^(300)gt 5^(200)gt 4^(250)gt 2^(350)`
D. None of these

Answer

To arrange the numbers \(2^{350}, 5^{200}, 3^{300}, 4^{250}\) in descending order, we can express all the terms with a common base. This will allow us to compare their magnitudes more easily.

### Step-by-Step Solution:

1. **Convert all terms to base 2:**
- \(2^{350}\) remains as is.
- \(5^{200}\) can be rewritten using logarithms:
\[ 5^{200} = (2^{\log_2(5)})^{200} = 2^{200 \cdot \log_2(5)} \]
- \(3^{300}\) can also be rewritten:
\[ 3^{300} = (2^{\log_2(3)})^{300} = 2^{300 \cdot \log_2(3)} \]
- \(4^{250}\) can be rewritten since \(4 = 2^2\):
\[ 4^{250} = (2^2)^{250} = 2^{500} \]

2. **Now we have:**
- \(2^{350}\)
- \(2^{200 \cdot \log_2(5)}\)
- \(2^{300 \cdot \log_2(3)}\)
- \(2^{500}\)

3. **Compare the exponents:**
- We need to compare \(350\), \(200 \cdot \log_2(5)\), \(300 \cdot \log_2(3)\), and \(500\).
- Calculate \(200 \cdot \log_2(5)\):
\[ \log_2(5) \approx 2.32193 \implies 200 \cdot \log_2(5) \approx 464.386 \]
- Calculate \(300 \cdot \log_2(3)\):
\[ \log_2(3) \approx 1.58496 \implies 300 \cdot \log_2(3) \approx 475.488 \]

4. **List the values for comparison:**
- \(350\)
- \(464.386\) (from \(5^{200}\))
- \(475.488\) (from \(3^{300}\))
- \(500\) (from \(4^{250}\))

5. **Arrange in descending order based on the exponent values:**
- \(500\) (from \(4^{250}\))
- \(475.488\) (from \(3^{300}\))
- \(464.386\) (from \(5^{200}\))
- \(350\) (from \(2^{350}\))

6. **Final arrangement of the original terms:**
- \(4^{250}\)
- \(3^{300}\)
- \(5^{200}\)
- \(2^{350}\)

### Conclusion:
The numbers in descending order are:
\[ 4^{250}, 3^{300}, 5^{200}, 2^{350} \]